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Pumping effects in models of periodically forced flow configurations. (English) Zbl 1136.76338
Summary: A periodically forced system of differential equations is defined to be a pump, if there exists an asymptotically periodic solution with non-equilibrium mean. It is proved that such systems exist. The definition is based on physical and numerical observations of pumping in (models of) asymmetric flow configurations. For models with rigid pipes and tanks, physical explanations for the pumping effects are derived. One of the pumps is an internally forced linear system. For externally forced nonlinear rigid pipe models, necessary and sufficient conditions for pumping are given. It is then demonstrated in a general setting that no externally forced linear pump exists.

MSC:
76B99 Incompressible inviscid fluids
34C25 Periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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